This paper presents the development of simplified manipulator dynamic models which satisfy the desired steady-state error specification in the joint-variable space or in the Cartesian space under a nonlinear decoupled controller. The formulae which relate the tracking errors of joint variables in the joint-variable space or the manipulator hand in the Cartesian space to the dynamic modeling errors are first developed. Using these formulae, we derive the maximum error tolerance for each dynamic coefficient of the equations of motion. Then each simplified dynamic coefficient of the equations of motion can be expressed as a linear combination of the product terms of sinusoidal and polynomial basis functions. To illustrate the approach, a computer simulation has been carried out to obtain two simplified dynamic models of a Stanford robot arm which satisfy the specified error tolerances in the joint-variable space and in the Cartesian space under respective nonlinear decoupled controllers. Finally, to measure the time complexity of simplified models, the number of mathematical operations in terms of multiplication and addition for computing the joint torques is tabulated and discussed with the parallel computation result of Newton-Euler equations of motion.
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